Property $$P_{naive}$$ P naive for acylindrically hyperbolic groups

Property $$P_{naive}$$ P naive for acylindrically hyperbolic groups Math. Z. https://doi.org/10.1007/s00209-018-2094-1 Mathematische Zeitschrift Property P for acylindrically hyperbolic groups naive 1 2 Carolyn R. Abbott · François Dahmani Received: 2 September 2017 / Accepted: 13 April 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract We prove that every acylindrically hyperbolic group that has no non-trivial finite normal subgroup satisfies a strong ping pong property, the P property: for any finite nai ve collection of elements h ,..., h , there exists another element γ = 1 such that for all 1 k i, h ,γ=h ∗γ . We also show that if a collection of subgroups H ,..., H is a i i 1 k hyperbolically embedded collection, then there is γ = 1 such that for all i,  H ,γ = H ∗γ . i i Keywords Acylindrically hyperbolic groups · δ-hyperbolic spaces · C -algebras · Free subgroups · Ping-pong lemma · Property P nai ve Mathematics Subject Classification 20E07 · 20F65 · 46L35 The Ping-Pong lemma and its many variations are iconic arguments in group theory that are particularly useful when dealing with groups acting on hyperbolic spaces. They allow one to produce free subgroups at will in many groups. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Property $$P_{naive}$$ P naive for acylindrically hyperbolic groups

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
D.O.I.
10.1007/s00209-018-2094-1
Publisher site
See Article on Publisher Site

Abstract

Math. Z. https://doi.org/10.1007/s00209-018-2094-1 Mathematische Zeitschrift Property P for acylindrically hyperbolic groups naive 1 2 Carolyn R. Abbott · François Dahmani Received: 2 September 2017 / Accepted: 13 April 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract We prove that every acylindrically hyperbolic group that has no non-trivial finite normal subgroup satisfies a strong ping pong property, the P property: for any finite nai ve collection of elements h ,..., h , there exists another element γ = 1 such that for all 1 k i, h ,γ=h ∗γ . We also show that if a collection of subgroups H ,..., H is a i i 1 k hyperbolically embedded collection, then there is γ = 1 such that for all i,  H ,γ = H ∗γ . i i Keywords Acylindrically hyperbolic groups · δ-hyperbolic spaces · C -algebras · Free subgroups · Ping-pong lemma · Property P nai ve Mathematics Subject Classification 20E07 · 20F65 · 46L35 The Ping-Pong lemma and its many variations are iconic arguments in group theory that are particularly useful when dealing with groups acting on hyperbolic spaces. They allow one to produce free subgroups at will in many groups.

Journal

Mathematische ZeitschriftSpringer Journals

Published: Jun 5, 2018

References

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